Question

The binary relation $R=\left\{\right(1,1),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4\left)\right\}$ on the set $A=\{1,2,3,4\}$ is

• A. Reflexive, symmetric and transitive
• B. Neither reflexive, nor irreflexive but transitive
• C. Irreflexive, symmetric and transitive
• D. Irreflexive and antisymmetric

Answer 1

The correct option is B Neither reflexive, nor irreflexive but transitive

The relation $R$ doesn't contain (4, 4), so $R$ is not reflexive relation.
Since relation $R$ contains $(1,1),(2,2)$ and $(3,3)$.
Therefore, relation $R$ is also not irreflexive.
That $R$ is transitive, can be checked by systematically checking for all $(a,b)$ and $(b,c)$ in $R$, whether $(a,c)$ also exists in $R$.
So, option (b) is correct.